The Rational Number Property | Understanding the Sum and Product of Rational Numbers

sum or product of two rational numbers is

The sum or product of two rational numbers is also a rational number

The sum or product of two rational numbers is also a rational number.

To understand why this is true, let’s start by defining what rational numbers are. A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers. For example, 3/4, -2/5, and 7 are all rational numbers.

Now, let’s consider the sum of two rational numbers. Suppose we have two rational numbers, a/b and c/d. To find their sum, we need to add the numerators and keep the same denominator. The sum would be (a/b) + (c/d) = (ad + bc)/bd. Since the numerators and denominators are both integers (ad + bc is the sum of two integers and bd is the product of two integers), the sum is still a fraction with integer values in both the numerator and denominator. Hence, the sum of two rational numbers is a rational number.

Next, let’s consider the product of two rational numbers. If we have two rational numbers, a/b and c/d, their product is given by (a/b) × (c/d) = (ac)/(bd). Again, the numerator (ac) and denominator (bd) are both integers because they are products of two integers, which means the product is also a rational number.

Therefore, both the sum and the product of two rational numbers will always be rational numbers.

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